Gas Detection Systems and Methods Using Measurement Position Uncertainty Representations

ABSTRACT

In some embodiments, a natural gas leak detection system generates display content including indicators of remote and local potential leak source areas situated on a map of an area of a gas concentration measurement survey performed by a vehicle-borne device. The remote area may be shaped as a wedge extending upwind from an associated gas concentration measurement point. The local area graphically represents a potential local leak source area situated around the gas concentration measurement point, and having a boundary within a predetermined distance (e.g. 10 meters) of the gas concentration measurement point. The local area may be represented as a circle, ellipse, or other shape, and may include an area downwind from the measurement point. Size and/or shape parameters of the local area indicator may be determined according to survey vehicle speed and direction data, and/or wind speed and direction data characterizing the measurement point.

RELATED APPLICATION DATA

This application is a continuation of U.S. patent application Ser. No.14/948,287, filed on Nov. 21, 2015, entitled “Gas Detection Systems andMethods Using Measurement Position Uncertainty Representations,” whichis scheduled to issue on Mar. 24, 2020 as U.S. Pat. No. 10,598,562, andwhich claims the benefit of the filing date of U.S. provisional patentapplication No. 62/083,084, filed on Nov. 21, 2014, entitled “GasDetection Systems and Methods Using Wind and Vehicle SpeedMeasurements,” the entire contents of both of which are incorporated byreference herein.

BACKGROUND

The invention relates to systems and methods for detecting gas leakssuch as methane gas leaks.

A common means of distributing energy around the world is by thetransmission of gas, usually natural gas. In some areas of the worldmanufactured gasses are also transmitted for use in homes and factories.Gas is typically transmitted through underground pipelines havingbranches that extend into homes and other buildings for use in providingenergy for space and water heating. Many thousands of miles of gaspipeline exist in virtually every major populated area. Since gas ishighly combustible, gas leakage is a serious safety concern. Recently,there have been reports of serious fires or explosions caused by leakageof gas in the United States as the pipeline infrastructure becomesolder. For this reason, much effort has been made to provideinstrumentation for detecting small amounts of gas so that leaks can belocated to permit repairs.

Conventionally, search teams are equipped with gas detectors to locate agas leak in the immediate proximity of the detector. When the plume ofgas from a leak is detected, the engineers may walk to scan the areaslowly and in all directions by trial and error to find the source ofthe gas leak. This process may be further complicated by wind thatquickly disperses the gas plume. Such a search method is time consumingand often unreliable, because the engineer walks around with little orno guidance while trying to find the source of the gas leak.

Another approach to gas leak detection is to mount a gas leak detectioninstrument on a moving vehicle, e.g., as considered in U.S. Pat. No.5,946,095. A natural gas detector apparatus is mounted to the vehicle sothat the vehicle transports the detector apparatus over an area ofinterest at speeds of up to 20 miles per hour. The apparatus is arrangedsuch that natural gas intercepts a beam path and absorbs representativewavelengths of a light beam. A receiver section receives a portion ofthe light beam onto an electro-optical etalon for detecting the gas.Although a moving vehicle may cover more ground than a surveyor on foot,there is still the problem of locating the gas leak source (e.g., abroken pipe) if a plume of gas is detected from the vehicle. Thus, thereis still a need to provide a method and apparatus to locate the sourceof a gas leak quickly and reliably.

SUMMARY

According to one aspect, a natural gas leak detection system comprisesat least one hardware processor and associated memory configured togenerate display content according to gas concentration and associatedwind direction and wind magnitude data characterizing a gasconcentration measurement run performed by a mobile gas concentrationmeasurement device; and a display device coupled to the at least onehardware processor and associated memory, the display device configuredto present the display content. The display content comprises at leastone angular search area indicator situated on a street map, and a localpotential leak source area indicator situated on the map. The searcharea indicator has an axis indicating a representative wind directionrelative to a geo-referenced location of at least one gas concentrationmeasurement point. The search area indicator also has a width relativeto the axis, wherein the width is indicative of a wind directionvariability associated with a plurality of wind direction measurementsin an area of the gas concentration measurement point. The localpotential leak source area indicator is situated on the map. The localpotential leak source area indicator graphically represents a potentiallocal leak source area situated around the gas concentration measurementpoint and having a boundary within 10 meters of the gas concentrationmeasurement point.

According to another aspect, a non-transitory computer-readable mediumencodes instructions which, when executed by at least one hardwareprocessor and associated memory, cause the at least one hardwareprocessor and associated memory to generate display content forpresentation on a display device, the display content being generatedaccording to gas concentration and associated wind direction and windmagnitude data characterizing a gas concentration measurement runperformed by a mobile gas concentration measurement device. The displaycontent comprises at least one angular search area indicator situated ona street map, and a local potential leak source area indicator situatedon the map. The search area indicator indicates a search area suspectedto have a natural gas leak source, the search area indicator having anaxis indicating a representative wind direction relative to ageo-referenced location of at least one gas concentration measurementpoint, and the search area indicator having a width relative to theaxis, wherein the width is indicative of a wind direction variabilityassociated with a plurality of wind direction measurements in an area ofthe gas concentration measurement point. The local potential leak sourcearea indicator is situated on the map. The local potential leak sourcearea indicator graphically represents a potential local leak source areasituated around the gas concentration measurement point and having aboundary within 10 meters of the gas concentration measurement point.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing aspects and advantages of the present invention willbecome better understood upon reading the following detailed descriptionand upon reference to the drawings where:

FIG. 1 shows a gas leak detection apparatus according to someembodiments of the present invention.

FIG. 2 illustrates hardware components of a computer system according tosome embodiments of the present invention.

FIG. 3 shows a number of application or modules running on a clientcomputer system and a corresponding server computer system according tosome embodiments of the present invention.

FIG. 4 is a schematic drawing of a screen shot on a graphical userinterface displaying survey results on a street map according to someembodiments of the present invention.

FIG. 5 is a schematic drawing of a screen shot on a graphical userinterface with GPS indicators according to some embodiments of thepresent invention.

FIG. 6 is a schematic drawing of a screen shot on a graphical userinterface with weather station status indicators according to someembodiments of the present invention.

FIG. 7 is a schematic drawing of a screen shot on a graphical userinterface with map controls according to some embodiments of the presentinvention.

FIG. 8 is a schematic diagram of three search area indicators accordingto some embodiments of the present invention.

FIG. 9 is a schematic diagram illustrating wind lines relative to thepath of a mobile gas measurement device for detecting or not detecting agas leak from a potential gas leak source according to some embodimentsof the present invention.

FIG. 10 is a schematic diagram of wind direction and a path of a mobilegas measurement device used to estimate a probability of detection of agas leak from a potential gas leak source at one or more measurementpoints along the path according to some embodiments of the presentinvention.

FIG. 11 is a graph of probability density vs. wind directions forestimating a probability of detection of a gas leak from a potential gasleak source according to some embodiments of the present invention.

FIG. 12 is a flow chart showing steps for performing a gas leak surveyaccording to some embodiments of the present invention.

FIG. 13 is a flow chart showing steps for generating a search areaindicator according to some embodiments of the present invention.

FIG. 14 is a flow chart showing steps for calculating a boundary of asurvey area according to some embodiments of the present invention.

FIG. 15 is a flow chart showing steps for displaying layers overlaid orsuperimposed on a street map according to some embodiments of thepresent invention.

FIG. 16 is a graph of vertical dispersion coefficients of a gas plume asa function of downwind distance from a gas leak source according to someembodiments of the present invention.

FIG. 17 is a graph of crosswind dispersion coefficients of a gas plumeas a function of downwind distance from a gas leak source according tosome embodiments of the present invention.

FIG. 18 is a table of dispersion coefficients for various atmosphericconditions according to some embodiments of the present invention.

FIG. 19 illustrates an exemplary relationships between a reference(fixed) direction, a wind direction, and a wind direction variabilityand/or uncertainty indicator according to some embodiments of thepresent invention.

FIG. 20 shows an exemplary dual-zone search area indicator comprising anangular search area indicator and a positional uncertainty indicatoraccording to some embodiments of the present invention.

FIG. 21 illustrates an exemplary reconstructed wind bearing uncertaintyas a function of vehicle speed for a fixed wind bearing and fivedifferent wind speed values according to some embodiments of the presentinvention.

FIG. 22 shows computed values of a number of parameters for threeexemplary wind speeds according to some embodiments of the presentinvention.

FIG. 23 shows an exemplary computed (simulated) pointing uncertainty andan associated analytical function as a function of wind speed for avehicle speed of 10 m/s according to some embodiments of the presentinvention.

FIG. 24 shows an angular search area indicator and an associatedpositional uncertainty indicator, as well as a survey area indicator,all superimposed on a map display according to some embodiments of thepresent invention.

FIG. 25 shows an exemplary sequence of steps performed by at least oneprocessor to generate a display according to determined variability andmeasurement uncertainty indicators, according to some embodiments of thepresent invention.

DETAILED DESCRIPTION

Apparatus and methods described herein may include or employ one or moreinterconnected computer systems such as servers, personal computersand/or mobile communication devices, each comprising one or moreprocessors and associated memory, storage, input and display devices.Such computer systems may run software implementing methods describedherein when executed on hardware. In the following description, it isunderstood that all recited connections between structures can be directoperative connections or indirect operative connections throughintermediary structures. A set of elements includes one or moreelements. Any recitation of an element is understood to refer to atleast one element. A plurality of elements includes at least twoelements. Unless otherwise required, any described method steps need notbe necessarily performed in a particular illustrated order. A firstelement (e.g. data) derived from a second element encompasses a firstelement equal to the second element, as well as a first elementgenerated by processing the second element and optionally other data.Making a determination or decision according to a parameter encompassesmaking the determination or decision according to the parameter andoptionally according to other data. Unless otherwise specified, anindicator of some quantity/data may be the quantity/data itself, or anindicator different from the quantity/data itself. Computer programsdescribed in some embodiments of the present invention may bestand-alone software entities or sub-entities (e.g., subroutines, codeobjects) of other computer programs. Computer readable media encompassstorage (non-transitory) media such as magnetic, optic, andsemiconductor media (e.g. hard drives, optical disks, flash memory,DRAM), as well as communications links such as conductive cables andfiber optic links. According to some embodiments, the present inventionprovides, inter alia, computer systems programmed to perform the methodsdescribed herein, as well as computer-readable media encodinginstructions to perform the methods described herein.

FIG. 1 shows a gas leak detection system 10 according to someembodiments of the present invention. System 10 comprises a serviceprovider server computer system 12 and a set of client computer systems18 a-c all connected through a wide area network 16 such as theInternet. Client computer systems 18 a-c may be personal computers,laptops, smartphones, tablet computers and the like. A vehicle 24 suchas an automobile may be used to carry at least some client computersystems (e.g. an exemplary client computer system 18 c) and associatedhardware including a mobile gas measurement device 26, a location/GPSmeasurement device 30, and a wind measurement device 32. In a preferredembodiment, the mobile gas measurement device 26 may be a Picarroanalyzer using Wavelength-Scanned Cavity Ring Down Spectroscopy (CRDS),available from Picarro, Inc., Santa Clara, Calif. Such analyzers may becapable of detecting trace amounts of gases such as methane, acetylene,carbon monoxide, carbon dioxide, hydrogen sulfide, and/or water. Inparticular applications suited for detection of natural gas leaks, aPicarro G2203 analyzer capable of detecting methane concentrationvariations of 3 ppb may be used. Wind measurement device 32 may includea wind anemometer and a wind direction detector (e.g. wind vane). GPSmeasurement device 30 may be a stand-alone device or a device built intoclient computer system 18 c.

FIG. 2 schematically illustrates a plurality of hardware components thateach computer system 18 may include. Such computer systems may bedevices capable of web browsing and have access to remotely-hostedprotected websites, such as desktop, laptop, tablet computer devices, ormobile phones such as smartphones. In some embodiments, computer system18 comprises one or more processors 34, a memory unit 36, a set of inputdevices 40, a set of output devices 44, a set of storage devices 42, anda communication interface controller 46, all connected by a set of buses38. In some embodiments, processor 34 comprises a physical device, suchas a multi-core integrated circuit, configured to execute computationaland/or logical operations with a set of signals and/or data. In someembodiments, such logical operations are delivered to processor 34 inthe form of a sequence of processor instructions (e.g. machine code orother type of software). Memory unit 36 may comprise random-accessmemory (RAM) storing instructions and operands accessed and/or generatedby processor 34. Input devices 40 may include touch-sensitiveinterfaces, computer keyboards and mice, among others, allowing a userto introduce data and/or instructions into system 18. Output devices 44may include display devices such as monitors. In some embodiments, inputdevices 40 and output devices 44 may share a common piece of hardware,as in the case of touch-screen devices. Storage devices 42 includecomputer-readable media enabling the storage, reading, and writing ofsoftware instructions and/or data. Exemplary storage devices 42 includemagnetic and optical disks and flash memory devices, as well asremovable media such as CD and/or DVD disks and drives. Communicationinterface controller 46 enables system 18 to connect to a computernetwork and/or to other machines/computer systems. Typical communicationinterface controllers 46 include network adapters. Buses 38 collectivelyrepresent the plurality of system, peripheral, and chipset buses, and/orall other circuitry enabling the inter-communication of devices 34-46 ofcomputer system 18.

FIG. 3 shows a number of applications or modules running on an exemplaryclient computer system 18 and corresponding server computer system 12.Authentication applications 54, 62 are used to establish securecommunications between computer systems 12, 18, allowing client computersystem 18 selective access to the data of a particular customer or useraccount. A client data collection module 56 collects real-time gasconcentration, location data such as global positioning system (GPS)data, as well as wind speed and wind direction data. A graphical userinterface (GUI) module 58 is used to receive user input and displaysurvey results and other GUI displays to system users. A client-sidereal-time data processing module 60 may be used to perform at least someof the data processing described herein to generate survey results frominput data. Data processing may also be performed by a server-side dataprocessing module 68. Server computer system 12 also maintains one ormore application modules and/or associated data structures storingcurrent and past survey results 64, as well as application modulesand/or data structures storing reference data 66 such as platsindicating the geographic locations of natural gas pipelines.

FIG. 4 is a schematic drawing of a screen shot on a graphical userinterface, displaying survey results on a street map 70 according tosome embodiments of the present invention. The GUI screenshots are mostpreferably displayed on a client device in the vehicle, which may beconnected to a server as described above. The illustrated screenshotsshow both exemplary user input, which may be used to control systemoperation, and exemplary real-time displays of collected/processed data.In the example, it includes the geo-referenced street map 70 showingplat lines 72. The plat lines 72 are preferably derived from gas companyrecords. An active pipeline plat boundary 71 may also be displayed onthe map 70. A user-selectable button 96 may be selected to overlay aselected pipeline plat on the map 70. Superimposed on the map 70 are oneor more lines (preferably in a distinguishing color not shown in patentdrawings) indicating the path 74 driven by the vehicle with the mobilegas measurement device on one or more gas survey routes. In thisexample, the path 74 shows the vehicle U-turned at the Y-shapedintersection. Optionally, a current location icon 75 may be overlaid onthe map 70 to indicate the current surveyor location, e.g., the positionof the vehicle with a gas measurement device and wind measurementdevice. A user-selectable button 94 may be selected to center the map 70by current surveyor location. Also provided is a user-selectable startbutton 102 and stop button 100 to start/stop capturing gas for analysis.An analyzer control button 104 is user-selectable to control analyzeroperations (e.g., shut down, start new trace, run isotopic analysis,etc.).

Peak markers 76 show the locations along the path 74 where peaks in thegas concentration measurements, which satisfy the conditions for beinglikely gas leak indications, were identified. The colors of the peakmarkers 76 may be used to distinguish data collected on different runs.The annotations within the peak markers 76 show the peak concentrationof methane at the locations of those measurement points (e.g., 3.0, 2.6,and 2.0 parts per million). An isotopic ratio marker 77 may be overlaidon the map 70 to indicate isotopic ratio analysis output and tolerance(e.g., −34.3+/−2.2). Also displayed on the map 70 are search areaindicators 78, preferably shown as a sector of a circle having adistinguishing color. Each of the search area indicators 78 indicates asearch area suspected to have a gas leak source. The opening angle ofthe search area indicator 78 depicts the variability in the winddirection. The axis of the search area indicator 78 (preferably an axisof symmetry) indicates the likely direction to the potential gas leaksource. Also displayed on the map 70 are one or more survey areaindicators 80 (shown as hatched regions in FIG. 4) that indicate asurvey area for a potential gas leak source. The survey area indicator80 adjoins the path 74 and extends in a substantially upwind directionfrom the path. The survey area marked by each indicator 80 is preferablydisplayed as a colored swath overlaid or superimposed on the map 70. Forexample, the colored swaths may be displayed in orange and green for tworuns. In preferred embodiments, the parameters of the search areaindicators 78 and the survey area indicators 80 (described in greaterdetail with reference to FIGS. 8-11 below) are derived from measurementsof the wind, the velocity of the vehicle, and optionally the prevailingatmospheric stability conditions.

Referring still to FIG. 4, the surveyor user interface also preferablyincludes a real-time CH4 concentration reading 82. A wind indicatorsymbol 84 preferably displays real-time wind information, which may becorrected for the velocity vector of the vehicle to represent the truewind rather than the apparent wind when the vehicle is in motion.Average wind direction is preferably indicated by the direction of thearrow of the wind indicator symbol 84, while wind direction variabilityis indicated by the degree of open angle of the wedge extending from thebottom of the arrow. Wind speed is preferably indicated by the length ofthe arrow in the wind indicator symbol 84. An internet connectionindicator 98 blinks when the internet connection is good. A datatransfer status button 86 is user-selectable to display data transferstatus (e.g., data transfer successful, intermittent data transfer, ordata transfer failed). An analyzer status button 88 is user-selectableto display current analyzer status such as cavity pressure, cavitytemperature, and warm box temperature. A map control button 106 isuser-selectable to open a map controls window with user-selectable layeroptions, discussed below with reference to FIG. 7.

FIG. 5 is a schematic drawing of a screen shot on the graphical userinterface, displaying a GPS status window 91, according to someembodiments of the present invention. A user-selectable GPS statusbutton 90 may be selected to open the GPS status window 91. The GPSstatus window 91 preferably includes indicators of the current GPSstatus, such as “GPS OK”, “Unreliable GPS signal”, “GPS Failed”, or “GPSNot Detectable”.

FIG. 6 is a schematic drawing of a screen shot on the graphical userinterface, displaying a weather station status window 93, according tosome embodiments of the present invention. A user-selectable weatherstation status button 92 may be selected to open the weather stationstatus window 93. The weather station status window 93 preferablyincludes indicators of the current weather station status, such as“Weather Station OK”, “Weather Station Failed”, or “Weather Station NotDetectable”. Weather station data are preferably received in real-timeand may include wind data and atmospheric stability conditions datarelevant to the area being surveyed.

FIG. 7 is a schematic drawing of a screen shot on the graphical userinterface, displaying a map control window 95. Various elementsdisplayed on the map 70 are regarded as layers which may be turned on oroff. In this example, map controls window 95 includes sixuser-selectable buttons named “Hide Peak Markers”, “Hide Search AreaIndicators”, “Minimum Amplitude”, “Hide Isotopic Analysis”, “Hide Fieldof View”, and “Hide Plat Outline”. The “Hide Peak Markers” button may beselected so that the markers indicating peak gas concentrationmeasurements are not displayed on the map 70. The “Hide Search AreaIndicators” button may be selected so that the search area indicatorsare not displayed on the map 70. The “Minimum Amplitude” button may beselected so that gas concentration peaks not meeting a minimum amplituderequirement are not displayed on the map 70. The “Hide IsotopicAnalysis” button may be selected so that isotopic ratio analysisinformation is not displayed on the map 70 next to the peak markers. The“Hide Field of View” button may be selected so that the survey areaindicator(s) are not displayed on the map 70. The “Hide Plat Outline”button may be selected so that the plat lines are not displayed on themap 70.

FIG. 8 is a schematic diagram of three search area indicators 78 a, 78b, and 78 c according to some embodiments of the present invention. Eachof the search area indicators 78 a, 78 b, and 78 c has a respective axis108 a, 108 b, and 108 c indicating a representative wind directionrelative to a geo-referenced location of a corresponding gasconcentration measurement point M1, M2, and M3. The gas concentrationmeasurement points M1, M2, and M3 are positioned along the path 74traveled by the vehicle 24 that carries a GPS device, a mobile gasmeasurement device, and wind measurement device for taking winddirection measurements and wind speed measurements. Each of the searcharea indicators, such as the search area indicator 78 c, preferably hasa width W relative to its axis 108 c. The width W is indicative of awind direction variability associated with wind direction measurementsin the area of the gas concentration measurement point M3. In preferredembodiments, the width W is indicative of a variance or standarddeviation of the wind direction measurements. Also in preferredembodiments, the search area indicator 78 c has the shape of a sector ofa circle, with the center of the circle positioned on the map at thelocation of the gas concentration measurement point M3. Most preferably,the angle A subtended by the sector of the circle is proportional to astandard deviation of the wind direction measurements taken at or nearbythe measurement point M3. For example, the angle A may be set to a valuethat is twice or four times the angular standard deviation of the winddirection measurements. It is not necessary to display the gasconcentration measurement points M1, M2, and M3 on the map along withthe search area indicators 78 a, 78 b, and 78 c. As previously shown inFIGS. 4 and 7, the measurement points and associated gas concentrationmeasurements are preferably map layer options for an end-user that maybe turned on or off.

Referring again to FIG. 8, the axis 108 c of the search area indicator78 c is preferably an axis of symmetry and points in a representativewind direction relative to the gas concentration measurement point M3.The representative wind direction is preferably a mean, median or modeof the wind direction measurements taken at or nearby the measurementpoint M3, and indicates the likely direction to a potential gas leaksource. The wind direction measurements may be taken from the vehicle 24as it moves and converted to wind direction values relative to theground (e.g., by subtracting or correcting for the velocity vector ofthe vehicle). In some embodiments, the axis 108 c has a length Lindicative of a maximum detection distance value representative of anestimated maximum distance from a potential gas leak source at which agas leak from the source can be detected. For example, the length may beproportional to the maximum detection distance value, or proportional toa monotonically increasing function of the maximum detection distancevalue, such that longer maximum detection distance values arerepresented by longer axis lengths. In preferred embodiments, themaximum detection distance value and corresponding length L aredetermined according to data representative of wind speed in the searcharea. In some embodiments, the maximum detection distance value and thecorresponding length L are determined according to data representativeof atmospheric stability conditions in the search area. Each of thesearch area indicators 78 a, 78 b, and 78 c may thus provide a visualindication of a likely direction and estimated distance to a potentialgas leak source. Although a sector of a circle is the presentlypreferred shape for a search area indicator, alternative shapes for asearch area indicator include, but are not limited to, a triangle, atrapezoid, or a wedge.

FIG. 9 is a schematic diagram illustrating an example of detecting ornot detecting a gas leak from a potential gas leak source, according tosome embodiments of the present invention. An indicator of a survey area(also sometimes referred to as a “field of view”) is intended as anindication of how well the measurement process surveys the area aroundthe path 74 traveled by the vehicle 24 that carries a GPS device, amobile gas measurement device, and wind measurement device. The surveyarea indicator is designed such that if a potential gas leak source islocated in the survey area and has a rate of leakage meeting a minimumleak rate condition, then an estimated probability of detection of a gasleak from the potential gas leak source at one or more measurementpoints P along the path 74 satisfies a probability condition.

Whether or not a potential gas leak source of a given strength isdetectable by a gas measurement device of a given sensitivity depends onthe separation distance of the source from the gas measurement deviceand on whether the wind is sufficient to transport gas from the gas leaksource to the gas measurement device at some point along the path 74. Insome embodiments, a physical model is employed that relates the measuredgas concentration peak at the location of the vehicle 24 (in ppm, forexample) to the emission rate of the potential gas leak source (ing/sec, for example) and the distance between the source and thedetection point.

There are multiple possible models that describe the propagation of agas leak as a plume through the atmosphere. One well-validated physicalmodel for a plume (Gifford, F. A., 1959. “Statistical properties of afluctuating plume dispersion model”. Adv. Geophys, 6, 117-137) is tomodel the plume as a Gaussian distribution in the spatial dimensionstransverse to the wind direction, or (for a ground level source), theconcentration c (x, y, z) at a distance x downwind, y crosswind, and ata height z from a gas leak source of strength Q located on the ground isgiven by Equation (1):

$\begin{matrix}{{C\left( {x,y,z} \right)} = {\frac{Q}{\pi v\sigma_{y}\sigma_{z}}e^{{{{- y^{2}}/2}\sigma_{y}^{2}} - {{z^{2}/2}\sigma_{z}^{2}}}}} & (1)\end{matrix}$

where v is the speed of the wind, and the plume dispersion half-widthsσ_(y) and σ_(z) depend on x via functions that are empiricallydetermined for various atmospheric stability conditions.

If we consider the plume center, where y=z=0, the concentration at thecenter is given by Equation (2):

$\begin{matrix}{C_{peak}{= \frac{Q}{\pi v\sigma_{y}\sigma_{z}}}} & (2)\end{matrix}$

The dimensions of the Gaussian distribution horizontally and vertically,half-widths σ_(y) and σ_(z), increase with increasing distance from thesource. The amount they increase can be estimated from measurements ofwind speed, solar irradiation, ground albedo, humidity, and terrain andobstacles, all of which influence the turbulent mixing of theatmosphere. However, if one is willing to tolerate somewhat moreuncertainty in the distance estimation, the turbulent mixing of theatmosphere can be estimated simply from the wind speed, the time of day,and the degree of cloudiness, all of which are parameters that areavailable either on the vehicle 24 or from public weather databases inreal time. Using these available data, estimates of the Gaussian widthparameters can be estimated using the Pasquill-Gifford-Turner turbulencetyping scheme (Turner, D. B. (1970). “Workbook of atmospheric dispersionestimates”. US Department of Health, Education, and Welfare, NationalCenter for Air Pollution Control), or modified versions of this scheme.

For a given sensitivity of the gas measurement device, there is aminimum concentration which may be detected. Given a gas leak source ofstrength greater than or equal to the minimum concentration, the sourcewill be detected if it is closer than an estimated maximum distanceX_(max), where this is the distance such that σ_(y)σ_(z)=Q/(π vc). Ifthe wind is blowing gas directly from the gas leak source to the gasmeasurement device, the estimated maximum distance X_(max) is thedistance beyond which the source may be missed. This estimated maximumdetection distance may depend upon atmospheric stability conditions aswell as wind speed. The formula diverges to infinity when the wind speedis very small, so it is advisable to set a lower limit (e.g., 0.5 m/s)for this quantity.

The minimum leak rate Q_(min) is determined by the requirements of theapplication. For natural gas distribution systems, a minimum leak rateof 0.5 scfh (standard cubic feet per hour) may be used; below thislevel, the leak may be considered unimportant. Other minimum leaks rates(e.g. 0.1 scfh, 1 scfh, or other values within or outside this range)may be used for natural gas or other leak detection applications. Theminimum detection limit of the plume C_(min) is given either by the gasdetection instrument technology itself, or by the spatial variability ofmethane in the atmosphere when leaks are not present. A typical valuefor C_(min) is 30 ppb (parts-per-billion) above the background level(typically 1,800 ppb). Given these two values for Q_(min) and C_(min),and by predicting σ_(y) and σ_(z) given atmospheric measurements (orwith specific assumptions about the state of the atmosphere, such as thestability class), one may then determine the estimated maximum detectiondistance X_(max) by determining the value for X_(max) that satisfies thefollowing equality, Equation (3):

$\begin{matrix}{{C_{\min} = \frac{Q_{\min}}{\pi v\sigma_{y}\sigma_{z}}}.} & (3)\end{matrix}$

In some embodiments the relationship between σ_(y) and σ_(z) and X_(max)is provided by a functional relationship, a lookup table, or similarmethod. Because σ_(y) and σ_(z) are monotonically increasing functionsof X_(max), a unique value can be determined from this process. Forexample, one useful functional form is a simple power law, where thecoefficients a, b, c, and d depend on atmospheric conditions:σ_(y)=ax^(b); σ_(z)=cx^(d).

In some embodiments, the concentration C measured close to the ground ofa Gaussian plume due to a gas leak source on the ground depends on therate of emission Q of the source, the distance x between the source andthe gas measurement device, and the speed of the wind blowing from thesource to the gas measurement device, in accordance with an expressionof the form (Equation 4):

$\begin{matrix}{C = \frac{Q}{\pi v{\sigma_{y}(x)}{\sigma_{z}(x)}}} & (4)\end{matrix}$

The expressions for σ_(y)(x) and σ_(z)(x) depend on the stability classof the atmosphere at the time of measurement. In some embodiments, thestability class of the atmosphere is inferred from the answers to a setof questions given to the operator, or from instruments of the vehicle,or from data received from public weather databases. As shown in thetable of FIG. 18, coefficients A, B, C, D, E and F may depend on surfacewind speed and atmospheric conditions such as day or night, incomingsolar radiation, and cloud cover. Mathematical forms for σ_(y)(x) andσ_(z)(x) are documented in Section 1.1.5 of the User's Guide forIndustrial Source Complex (ISC3), Dispersion Models Vol. 2 (USEnvironmental Protection Agency document EPA-454/B955-003b September1995). Given the sensitivity of the gas measurement device and the rateof emission of the smallest potential gas leak source of interest,equation (4) may be solved to find the estimated maximum distanceX_(max) beyond which a potential gas leak source may be missed by thegas measurement device.

FIG. 16 is a graph of vertical σ_(z)(x) dispersion coefficients of a gasplume as a function of downwind distance from a gas leak sourceaccording to some embodiments of the present invention. FIG. 17 is agraph of crosswind σ_(y)(x) dispersion coefficients of a gas plume as afunction of downwind distance from a gas leak source according to someembodiments of the present invention. The graphs are from from deNevers, 2000, Air Pollution Control Engineering, The McGraw-HillCompanies, Inc. The dispersion coefficients are functions of downwinddistance x. In this example, dispersion coefficients are calculatedbased on atmospheric stability. The table of FIG. 18 gives theatmospheric stability class as a function of wind speed, day or night,cloud cover, and solar radiation. In some embodiments, the dispersioncoefficients and/or the estimated maximum distance X_(max) may dependupon an urban or rural environment for the gas concentrationmeasurements and plume dispersion. For example, the estimated maximumdistance X_(max) may be less in an urban environment with buildings orother structures than in a rural environment.

The actual distance at which a gas leak source may be detected isreduced if there is some variability or uncertainty in the direction ofthe wind. This is because there is a probability that the wind blows gasin a direction such that it does not intercept the path 74 of thevehicle 24 (FIG. 9). In practice this uncertainty is usually larger thanthe intrinsic angular uncertainty σ_(y)/x implied by the Gaussian plumemodel. In order to determine the effective survey area of the mobile gasmeasurement device, assume for this example that the wind speed remainsapproximately constant within a time interval −T<t<T bounding the timet=0 at which the vehicle 24 passes through a particular point P on thepath 74, but that the wind direction (angle) is distributed as aGaussian with a known mean and standard deviation.

As shown in FIG. 9, we consider the line 110 through the measurementpoint P pointing toward the direction of the mean wind, and whether acandidate point Q on this line qualifies to be within the boundary ofthe survey area (i.e., within the field of view of the mobile gasmeasurement device of the vehicle 24). We also consider drawing a samplefrom the distribution of wind directions and drawing a line through thecandidate point Q in this direction. If this line intersects the path 74of the vehicle 24 within the time interval −T<t<T, and the distance fromthe candidate point Q to the point of intersection with the path 74 isless than or equal to the estimated maximum distance X_(max), then thisis regarded as detectable by the mobile gas measurement device since thepotential gas leak source at the candidate point Q would have beendetected along the path 74. The quantity T sets the time interval duringwhich it is expected to detect the gas coming from the candidate point Qat measurement point P. Theoretically, the time interval can be large,but it may not be reasonable to assume that the wind statistics remainunchanged for an extended period of time. In some embodiments, the winddirection measurements are taken during a time interval less than orequal to about 2 minutes, during which time interval a gas concentrationis measured at the gas concentration measurement point P. Morepreferably, the time interval is in the range of 10 to 20 seconds.

FIG. 10 is a schematic diagram showing the estimation of a probabilityof detection at the measurement point P of a gas leak from a potentialgas leak source at the candidate point Q, according to some embodimentsof the present invention. The probability of detection at measurementpoint P is estimated according to an angle θ subtended by a segment 79of the path 74 relative to the candidate point Q for the potential gasleak source. The path segment 79 is positioned within a distance of thecandidate point Q that is less than or equal to the estimated maximumdistance X_(max). The probability of detection is preferably estimatedaccording to a cumulative probability of wind directions with respect tothe subtended angle θ. The cumulative probability of wind directions maybe determined according to a representative wind direction (e.g., amean, median, or mode of the wind direction measurements) and a winddirection variability (e.g., variance or standard deviation) calculatedfrom the wind direction measurements.

The candidate point Q is deemed to be within the boundary of the surveyarea if the probability of successful detection of a potential gas leaksource at the candidate point Q, over the distribution of winddirections, satisfies a probability condition. In some embodiments, theprobability condition to be satisfied is an estimated probability ofsuccessful detection greater than or equal to a threshold value,typically set at 70%. In general, as the candidate point Q is moved afarther distance from the gas concentration measurement point P, therange of successful angles becomes smaller and the probability ofsuccess decreases, reaching a probability threshold at the boundary ofthe territory deemed to be within the survey area.

FIG. 11 is a graph of probability density vs. wind directions forestimating a probability of detection of a gas leak from a potential gasleak source, according to some embodiments of the present invention. Thearea under the curve spans a range of possible angles θ for thesuccessful detection of a potential gas leak from a candidate point. Theprobability density is preferably generated as a Gaussian or similardistribution from the calculated mean and standard deviation of the winddirection measurements in the area of the gas concentration measurementpoint P, FIG. 10. If the angle θ subtended by the path segment 79relative to the candidate point Q encompasses a percentage of possiblewind vectors that is greater than equal to a threshold percentage (e.g.,70%, although the percentage may be adjusted to other values such as50%, 60%, 67%, 75%, 80%, or 90% in some embodiments), and if thedistance from the candidate point Q to the measurement point P is lessthan the estimated maximum distance X_(max), then the candidate point Qis deemed to be within the survey area.

The above process is repeated as different measurement points along thepath 74 are chosen and different candidate points are evaluated for theprobability of successful detection of a potential gas leak source. Thecumulative distribution of the wind direction function together with aroot finding algorithm are useful for efficiently determining theboundary of the survey area. For example, referring again to FIG. 10,the root finding algorithm may consider candidate points along the lineof mean wind direction starting at the estimated maximum distanceX_(max) from measurement point P, and iteratively (e.g. using abisection or other method) moving closer to the measurement point Palong the mean wind direction line until the angle θ subtended by thepath segment 79 is sufficient to meet the probability threshold, asdetermined from the cumulative probability of wind directions over thesubtended angle θ, FIG. 11. Referring again to FIG. 4, the survey areaindicator 80 may be displayed on the map 70 as a colored “swath”adjoining the path 74 and extending in a substantially upwind directionfrom the path.

FIG. 12 is a flow chart showing a sequence of steps to perform a gasleak survey according to some embodiments of the present invention. Instep 200, the survey program is started, preferably by an operator inthe vehicle using a graphical user interface (GUI). The operator beginsto drive the vehicle on a survey route while the GUI displays a streetmap (FIG. 4). Gas concentration measurements are preferably performedrapidly along the survey route (e.g., at a rate of 0.2 Hz or greater,more preferably 1 Hz or greater). This enables the practice of drivingthe vehicle at normal surface street speeds (e.g., 35 miles per hour)while accumulating useful data. The gas concentration is measuredinitially as a function of time, and is combined with the output of theGPS receiver in order to obtain the gas concentration as a function ofdistance or location. Interpolation can be used to sample the data on aregularly spaced collection of measurement points. The concentration ofmethane typically varies smoothly with position, for the most part beingequal to the worldwide background level of 1.8 parts per milliontogether with enhancements from large and relatively distant sourcessuch as landfills and marshes.

In step 210, at least one processor (e.g. of a client device, serverdevice, or a combination) receives data representative of measured gasconcentrations, wind direction measurements, wind speed measurements,and GPS data. In decision block 220, it is determined if a peak in gasconcentration is identified. A peak may be identified from a gasconcentration measurement above a certain threshold (or within a certainrange), or exceeding background levels by a certain amount, which may bepredetermined or user-selected. In some embodiments, the gasconcentration and GPS data are analyzed using a peak-location method,and then each identified peak is subsequently fit (using linear ornonlinear optimization) for center and width. The functional form usedfor this fitting step may be a Gaussian pulse, since a Gaussian iscommonly the expected functional form taken by gas plumes propagatingthrough the atmosphere.

If a peak in gas concentration is not identified, then the programproceeds to step 250. If a peak in gas concentration is identified, thena peak marker is generated in step 230. The peak marker may be displayedon the map as a user-selectable layer, as previously discussed withreference to FIG. 4. In step 240, a search area indicator is generatedto indicate the likely location of a gas leak source corresponding tothe identified peak in gas concentration. The search area indicator maybe displayed on the map as a user-selectable layer, as shown in FIG. 4.In step 250, the survey area boundary is calculated, and a survey areaindicator may be displayed on the map as a user-selectable layer(hatched region in FIG. 4). In decision step 260, it is determined ifthe operator wishes to continue surveying (e.g., by determining if the“Stop Survey” button has been selected). If yes, the survey programreturns to step 210. If not, the survey results are stored in memory instep 270 (e.g., in the survey results 64 of FIG. 3), and the surveyprogram ends.

FIG. 13 is a flow chart showing a sequence of steps performed togenerate a search area indicator according to some embodiments of thepresent invention. When a local enhancement in the gas concentration isdetected, the likely direction and estimated distance to the potentialgas leak source is preferably calculated from data representative ofwind direction and wind speed measured during a time interval just priorto or during which the gas concentration was measured. The time intervalis preferably fewer than 2 minutes, and more preferably in the range of5 to 20 seconds. Calculating statistics from wind measurements mayrequire some conversion if the measurements are made using sensors on amoving vehicle. A sonic anemometer is preferably used to measure windalong two perpendicular axes. Once the anemometer has been mounted tothe vehicle, these axes are preferably fixed with respect to thevehicle. In step 241, wind speed and wind direction values that weremeasured relative to the vehicle are converted to wind speed and winddirection values relative to the ground by subtracting the velocityvector of the vehicle, as obtained from the GPS data. When the vehicleis stationary, GPS velocity may be ineffective for determining theorientation of the vehicle and wind direction, so it is preferable touse a compass (calibrated for true north vs. magnetic north) in additionto the anemometer.

In step 242, wind statistics are calculated from the converted windvalues to provide the parameters for the search area indicator. Thestatistics include a representative wind direction that is preferably amean, median, or mode of the wind direction measurements. The statisticsalso include a wind direction variability, such as a standard deviationor variance of the wind direction measurements. In step 243, an angularrange of search directions, extending from the location of the gasconcentration measurement point where the local enhancement wasdetected, is calculated according to the variability of the winddirection measurements. In optional step 244, atmospheric conditionsdata are received. Step 245 is determining a maximum detection distancevalue representative of the estimated maximum distance from thesuspected gas leak source at which a leak can be detected. In someembodiments, the maximum detection distance value is determinedaccording to Equation (3) or Equation (4), and the data representativeof wind speed and/or atmospheric stability conditions. Alternatively,the maximum detection distance value may be a predetermined number, auser-defined value, empirically determined from experiments, or a valueobtained from a look-up table. In step 246, the search area indicator isgenerated with the determined parameters, previously discussed withreference to FIG. 8.

FIG. 14 is a flow chart showing a sequence of step performed tocalculate a boundary of a survey area according to some embodiments ofthe present invention. In step 251, wind speed and wind direction valuesthat were measured relative to the vehicle are converted to wind speedand wind direction values relative to the ground by subtracting thevelocity vector of the vehicle, as previously described in step 241above. In optional step 252, atmospheric conditions data are received.Step 253 is determining a maximum detection distance valuerepresentative of the estimated maximum distance from a suspected gasleak source at which a leak can be detected. In some embodiments, themaximum detection distance value is determined according to Equation (3)or Equation (4), and the data representative of wind speed and/oratmospheric stability conditions. Alternatively, the maximum detectiondistance value may be a predetermined number, a user-defined value,empirically determined from experiments, or a value obtained from alook-up table. In step 254, it is determined what angle θ is subtendedby a segment of the path of the vehicle relative to the candidate pointQ for the potential gas leak source. The path segment is positionedwithin a distance of the candidate point Q that is less than or equal tothe estimated maximum distance.

In step 255, a representative wind direction (e.g., a mean, median, ormode of the wind direction measurements) and a wind directionvariability (e.g., variance or standard deviation) are calculated fromthe wind direction measurements. In step 256, the probability ofdetection is estimated according to a cumulative probability of winddirections with respect to the subtended angle θ. In step 257, thesurvey area boundary is calculated with a probability threshold. Forexample, if the angle θ subtended by the path segment relative to thecandidate point encompasses a percentage of possible wind vectors thatis greater than equal to a threshold percentage (e.g., 70%,), and if thedistance from the candidate point Q to the measurement point P is lessthan the estimated maximum distance X_(max), then the candidate point Qis deemed to be within the survey area. In decision step 258, it isdetermined if the survey area boundary function is to continue with thenext measurement point. If yes, steps 251-257 are repeated as differentmeasurement points along the path are chosen and different candidatepoints are evaluated for the probability of successful detection of apotential gas leak source. If not, then the boundary function ends.

FIG. 15 is a flow chart showing steps for displaying layers overlaid orsuperimposed on a street map according to some embodiments of thepresent invention. In step 310, a street map is displayed, preferably ona GUI visible to the operator in the vehicle. In step 320, the path ofthe vehicle with the mobile gas measurement device is displayed on themap. Various elements displayed on the map are regarded as layers whichmay be turned on or off. In this example, the map controls window (FIG.7) includes six user-selectable buttons named “Hide Peak Markers”, “HideSearch Area Indicators”, “Minimum Amplitude”, “Hide Isotopic Analysis”,“Hide Field of View”, and “Hide Plat Outline”. In decision step 330, itis determined if one or more of these layers is selected. If yes, theselected layer is displayed overlaid or superimposed on the street mapin step 340. If not, it is determined if the survey is to continue. Ifyes, display steps 310-350 are repeated. If not, the display options mayend.

The exemplary systems and methods described above allow a surveyor tolocate potential gas leak sources efficiently and effectively in highlypopulated areas. The search area indicators provide likely direction andestimated maximum distance to the source of detected gas leaks, whilethe survey area indicators provide an estimated statistical measure ofconfidence that an area was successfully surveyed for potential gasleaks. These aspects provide significant improvement in finding gas leaksources over conventional methods where engineers scan the area veryslowly and in all directions by trial and error to find the source of agas leak. These aspects also account for wind that may quickly dispersea gas plume.

Exemplary Systems and Methods Accounting for Uncertainties in Windand/or Position Measurements

In some embodiments, calculated uncertainties in wind and/or positionmeasurements are taken into account in one or more of the stepsdescribed herein, in particular to generate search area indicators asillustrated in FIGS. 4 and 8, survey area indicators as illustrated inFIGS. 4 and 9, and/or dual-zone search area indicators as illustrated inFIG. 20, described below.

Wind Direction Uncertainty

Consider the exemplary search area indicator 78 c shown in FIG. 8. Asnoted above, the search area indicator 78 c may have the shape of asector of a circle, with the center of the circle positioned on the mapat the location of the gas concentration measurement point M3. The angleA subtended by the sector of the circle may be proportional to astandard deviation of the wind direction measurements taken at or nearbythe measurement point M3. For example, the angle A may be set to a valuethat is twice or four times the angular standard deviation of the winddirection measurements.

Consider now the exemplary configuration shown in FIG. 19, wherein Nrepresents a reference direction (e.g. a North-South axis), and u is arepresentative wind direction. For example, u may be taken to the meandirection calculated over n samples, each characterized by an associatedwind direction u₁, u₂, . . . , u_(n). The angle α represents the anglebetween the reference and representative wind directions, while theangle θ represents the angle between the representative wind directionand the search area indicator boundary, i.e. θ=A/2, or half the angularextent of a search area indicator.

In some embodiments, a calculation of the angle θ (or A) may take intoaccount both a variability of wind direction measurements, as describedabove, and a determined uncertainty in measured wind direction withrespect to ground. For measurements taken using a moving vehicle, thewind speed and direction with respect to the ground are calculated byremoving the effect of the survey vehicle motion from the apparent windspeed and direction measured onboard the vehicle. Possible sources ofuncertainty in the wind direction with respect to the ground include,for example: the instrumental error of the wind sensor, the instrumentalerror of the sensor or system used to measure the speed of the vehicle,and compression or other distortion of the air stream at the locationwhere the wind measurement is made as the survey vehicle moves.

In some embodiments, a value of the angular extent θ is determinedaccording to a relation:

θ=β(σ_(variability) ²+σ_(uncertainty) ²)^(1/2)   (5)

wherein the variability term represents a variability (e.g. standarddeviation or similar measure) of values relative to the mean, while theuncertainty term is a function of the magnitudes of the wind speed u andcar speed v, for example

$\begin{matrix}{{\sigma_{variability} = \left( {\frac{1}{N}{\sum\limits_{i = 1}^{N}\left( {\overset{¯}{\alpha} - \alpha_{i}} \right)^{2}}} \right)^{1/2}},} & \left( {6A} \right)\end{matrix}$

with

$\overset{¯}{\alpha} = {\frac{1}{N}{\sum\limits_{i}\alpha_{i}}}$

representing the mean value of α_(i),

and

σ_(uncertainty) =f(u, v),   (6B)

for example

$\begin{matrix}{{\sigma_{uncertainty}{= {\min \left( {{180^{{^\circ}}},{a\frac{b + {cv}}{u + ɛ}}} \right)}}},} & \left( {6C} \right)\end{matrix}$

wherein α_(i) are measured wind directions each characterizing a sample,a, b, c, β and ε are parameter values, v represents a magnitude of avehicle velocity vector, and u represents a magnitude of a winddirection vector.

In some embodiments, the overall scaling factor β has a value between 1and 3, for example about 2. A larger overall scaling factor leads to theinclusion of a larger peripheral area in each search area indicator,while a smaller scaling factor leads to a narrower, more focused searcharea indicator.

The number N represents the number of samples used to generate a givensearch area indicator. In some embodiments, the number N has a fixed,peak-independent value. In some embodiments, the number N may depend onone or more determined characteristics of the peak, such as a spatialwidth of the peak and/or an estimate of a propagation distance (or time)for the plume. In general, the farther away a source is, the better adetermined average wind direction and directional variability describeshow good our knowledge of the true source direction is. Conversely, thecloser the source, and the narrower the width of the peak inconcentration, the more likely it is that an instantaneous winddirection indicates the direction to the source.

In some embodiments, a measurement uncertainty after averaging over nmeasurements may be determined as a function of the number ofmeasurements, for example

$\begin{matrix}{{\sigma_{uncertainty} = {\min \left( {{180{^\circ}},\frac{a}{\sqrt{n}},{\sum\limits_{i}\frac{b + {cv}_{i}}{u_{i}}}} \right)}},} & \left( {6D} \right)\end{matrix}$

which reduces to eq. (6C) for n=1. In other embodiments, the term a ineq. (6C) may be dependent on n, for example by including a 1/sqrt(n)factor such as the one illustrated in eq. (6D).

Eq. (6D) illustrates embodiments in which a measurement uncertainty iscalculated using a variable window, rather than a fixed window. In someembodiments, the averaging window may be chosen according to parameterssuch as peak width, wind speed, wind speed variability, wind directionvariability, and car trajectory parameters such as parameterscharacterizing changes in direction. For example, a shorter averagingwindow may be used for narrower peaks, since narrower peaks are morelikely to originate from nearby leaks, and in such cases aninstantaneous wind direction may better constrain the direction of theleak than wind direction measurements taken at more distant time points.Additionally, when the wind direction is less variable, less averagingtime may be needed to obtain a representative range of direction.Conversely, when the wind speed is low, the wind direction is likely tobe more variable, and a longer averaging time may be useful. Parametersbased on the trajectory of the car may be particularly useful in urbanareas such as urban canyons, where the true wind direction may changeabruptly after the survey vehicle turns onto a new street. In someembodiments, a shorter averaging window is used immediately after asharp (e.g. more than 45 degrees, or 90 degrees) turn is made, sinceolder wind measurement values are not representative of theinstantaneous wind direction and/or speed.

In some embodiments, using a variable measurement window as describedabove may affect the determination of parameters other than measurementuncertainty. Such parameters may include a representative winddirection, a determined wind direction variability, and/or otherparameters described above.

The minimum selection operation illustrated in eqs. (6C-D) may be usedto constrain the angular uncertainty to a maximum angle of 180 degrees.Such an angle implies that no direction is more likely than any other,i.e. that the wind direction is considered to contain no usefulinformation regarding the source location.

The parameters a, b, c, and ε may have empirically-determined valuesreflecting measurement uncertainties in a given experimental context. Inexemplary embodiments, an overall uncertainty scaling factor a has avalue between 0.5 and 1.5, a vehicle velocity added factor b has a valuebetween 0 and 1, a vehicle velocity scaling factor c has a value between1 and 5, and a wind velocity added factor ε has a value between 0.001and 0.1. In one exemplary embodiment, a, b, c, and ε have values ofabout 0.33, 0, 2 and 0.01, respectively.

In some embodiments, a magnitude of the uncertainty in the reconstructedtrue wind direction due to multiple sources of measurement error, aswell as its functional dependence on the speed of the vehicle and thetrue wind speed and direction with respect to the car's direction oftravel, may be determined using a Monte-Carlo simulation as describedbelow. In a single realization of the simulation, a particularcombination of a true vehicle velocity and true wind velocity is chosen.The effects of instrumental uncertainty on the measurements of carvelocity and apparent wind velocity may be simulated by introducingmeasurement errors, such as Gaussian errors, according to the knownspecifications of the measurement devices. The true wind speed anddirection are then reconstructed from the simulated noisy measurementsof vehicle velocity and apparent wind speed as described above. Multiplerealizations of the measurement are simulated for each combination oftrue wind and vehicle velocity. The uncertainty in the reconstructedtrue wind direction for a particular combination of true car velocityand true wind velocity may be taken to be the standard deviation of thedistribution of the reconstructed wind direction about the truedirection, or another indicator of the variability of the distribution.After performing the simulation for multiple combinations of true carvelocity and wind velocity, a functional form for the dependence ofreconstructed direction on wind speed and car speed may be generated.

In an exemplary embodiment, a simulated measurement error was determinedin the presence of two sources of error which were taken to be equal inmagnitude: the measurement error due to the wind sensor, describedabove, and a measurement error due to compression of the air streamabove the vehicle, as described below. Equation (6C) was found to be agood approximation of the functional dependence of the reconstructedtrue wind direction uncertainty for car speeds less than 20 m/s when thevalues 1, 0, 2, 0.01, were chosen for parameters a, b, c, and ε,respectively, for a single measurement, and 0.33-1/sqrt(10), 0, 2, 0.01for 10 measurements, respectively.

In some embodiments, wind sensors that employ ultrasonic time-of-flightor phase shift techniques often quote specs for measurement errors thatare proportional to the measured wind speed, with typical relativeuncertainties of 2% or better. We have found that the uncertainty in thespeed of the vehicle as determined using a series of timed locationmeasurements made with a high-precision (sub-meter) GPS system isusually much smaller than the measurement error given by common windsensor specifications. In addition, we have found that a correction tothe component of apparent wind speed in the direction of motion by asimple multiplicative factor can reasonably account for the effect ofthe compression of the airstream by the profile of the vehicle, and thatthe precision with which one can measure the correction factor istypically better than 2%. When taken together, such sources ofmeasurement error affect the uncertainty in the calculated true winddirection in a manner that increases approximately in proportion to carspeed and inversely with wind speed, according to the form of eq. (6C).

Eq. (6C) may be better understood by considering FIG. 21, which shows anexemplary reconstructed mean wind bearing uncertainty (in degrees) afterten measurements as a function of vehicle speed (in m/s) for fourdifferent wind speed values, and for a, b, c, and ε values of 0.33, 0, 2and 0.01, respectively, according to some embodiments of the presentinvention. As illustrated, the computed uncertainty increases withvehicle speed and decreases with wind velocity; the highestuncertainties correspond to high vehicle speeds and low wind velocities.For the sources of measurement error simulated here, we found that thereconstructed mean wind bearing uncertainty had a slight dependence onthe angle between the true wind direction and the direction of thevehicle's motion, which could be safely disregarded.

FIG. 22 shows computed values of a number of parameters for threeexemplary wind speeds according to some embodiments of the presentinvention. In particular, the derivative of uncertainty (eq. (6C)) withrespect to wind speed, dσ/dv, is equal to ac/u, or approximately 2/u forthe exemplary parameter values above. FIG. 22 illustrates how theresults of a simulation (e.g. Monte-Carlo simulation) can be used todeduce or confirm a dependence of the uncertainty term on car speed andwind speed.

FIG. 23 shows an exemplary computed (simulated) pointing uncertainty (indegrees) after ten measurements, as a function of wind speed (in m/s)for four vehicle speeds, according to some embodiments of the presentinvention. It can be seen that the computed pointing uncertaintyexhibits an inverse-dependence on wind speed as in equation 6C. We foundthat that the illustrated curves are sufficiently well described byequation 6C when the appropriate values of a, b, c and ε are chosen(0.33, 0, 2, and 0.01, respectively, for the curves of FIG. 23).

Local Potential Leak Source Area and Associated Peak PositionUncertainty

In some embodiments, a local potential leak source area is determinedand represented graphically as described below. The local potential leaksource area may represent an uncertainty in determined peak position andpotentially other sources of uncertainty, as described below. FIG. 20shows an exemplary dual-zone search area indicator 478 that includes anangular indicator 78 reflecting wind variability and/or measurementuncertainty as described above, and a local potential leak source areaindicator 499 graphically representing a potential local leak sourcearea situated around the gas concentration measurement point. In someembodiments, the area defined by local potential leak source areaindicator 499 has a boundary within a predetermined distance (e.g. 10meters) of the gas concentration measurement point. Local source areaindicator 499 may reflect an uncertainty in the geospatially-referencedposition determined to be associated with a peak event. Local sourcearea indicator 499 may have a rounded shape, e.g. a circle or an ellipsecentered at the determined event location. In some embodiments, a box(e.g. rectangular or square) or other sharp-angled shape may be used.Local source area indicator 499 reflects a probability of near- orunder-vehicle leaks, some of which may be present downwind from arecorded vehicle location. FIG. 24 shows an angular indicator 78 and anassociated local source area indicator 499, as well as a survey areaindicator 80, all superimposed on a map display, according to someembodiments of the present invention.

The area covered by local source area indicator 499 representsgraphically a physical, geospatially-referenced area where a potentialleak source may be located. In some embodiments, the size and/or shapeof local source area indicator 499 may be chosen according to one ormore survey parameters, as described below. In some embodiments, localsource area indicator 499 is formed by a circle or other symmetricalshape at vehicle speeds below a predetermined threshold, and by anellipse or other elongated shape at vehicle speeds above thepredetermined threshold. In other embodiments, local source areaindicator 499 may have the same shape at all speeds, with the size ofthe shape fixed or speed-dependent. In some embodiments, local sourcearea indicator 499 is a circle having a fixed radius corresponding to a90% containment area for near or under-vehicle leaks. Such a containmentarea may be determined empirically, by comparing where confirmedlocations of identified leaks are situated on a map relative to arecorded peak location. For example, local source area indicator 499 mayhave a radius between 10 and 30 feet, for example about 20 feet, forvehicle speeds below a threshold such as 30, 40, or 45 mph. For vehiclespeeds above the threshold, and in particular above 45 mph, which areabove those commonly used in leak surveys, local source area indicator499 may be shaped as an ellipse, with the longer ellipse axis along thedirection of motion reflecting the added positional uncertainty arisingfrom imperfect synchronization between location and concentrationmeasurements or other speed-dependent error source(s). For example, insome embodiments location and concentration measurements may besynchronized only to about 0.2-0.5 seconds, for example about 0.3seconds, which corresponds to a significant positional uncertainty athigh vehicle speeds. In some embodiments, local source area indicator499 is centered at the location of an identified peak event; in someembodiments, local source area indicator 499 may be weighted toward theupwind direction, i.e. have a larger extent upwind and a lesser extentdownwind from the associated peak location.

A measurement of concentration versus position involves the synthesis ofdata from two sources: a gas (e.g. methane) concentration analyzer, anda position determination system such as a GPS system. Both sub-systemsmeasure their respective data with respect to time, and may havedifferent reporting latencies, i.e. the time delays between the instanta measurement is made and the instant the measurement is reported acentral computer or data acquisition system. The two measurements aresynchronized in time in order to arrive at a result representingconcentration as a function of geospatially-referenced position.Consequently, an uncertainty in the timing delay calibration between thetwo measurements will propagate as an uncertainty in the location wherethe peak concentration is detected.

In some embodiments, we found that a timing offset between concentrationand position measurements can typically be found to a precision of 0.1to 1 second. With a survey vehicle velocity of 5 to 10×s per second,such a time offset translates into an error in the position of thedetected gas peak ranging from about 0.5 meters to about 10 meters. Sucha situation results in the possibility that leaks that lay on the pathof the survey vehicle may appear to fall outside of a purely-angulararea search area indicator, by appearing on a map to be downwind(behind) the peak concentration location as well as behind the angularsearch area wind indicator.

Furthermore, because of the finite accuracy of position measurement(GPS) systems, peak locations may tend to fall to the right or the leftof the track of the survey vehicle by a distance reflecting the accuracyof the location measurement. In some embodiments, the positionmeasurements can be made with an accuracy of about 1 meter or better. Inaddition, in some embodiments it was also found that, depending on thestrength of the wind (especially in light-wind situations), leaks may bedetected from distances of up to several meters downwind of the surveytrack, which can lead to a similar case as where the wind indicatoralone does not cover the leak location. This downwind distance dependson the magnitude of the mean wind relative to the turbulent windcomponents, which are driven by the stability of the atmosphere and/ornearby structures or terrain features. For example, this downwinddistance is largest under light wind conditions when the atmosphere isunstable, and is smallest when the mean wind is large and the atmosphereis stable. Within this distance, the gas from the leak can be detectedin all directions regardless of the mean wind. Outside of this distance,the mean wind dominates the transport and leaks in the downwinddirections can no longer be detected at the measurement point. Undertypical conditions, this distance ranges from less than a meter toseveral meters or more.

In addition, when depicting the location of the peak detection on a mapor satellite image, another source of uncertainty arises from how wellcertain features or geo-referenced points in the image can be mapped toactual geographical coordinates. In one embodiment, we found that themagnitude of this error can be up to several meters, and can be thedominant source of error in the depiction of the measured peak detectionposition.

Such uncertainty in position may be addressed by considering a searcharea to include, in addition to angular wind direction indicator 78(FIG. 20), a local source area indicator 499 centered at the peakdetection position. In some embodiments, local source area indicator 499may be shaped as an ellipse. In the following discussion, a circle maybe considered to be a special case of an ellipse, i.e. an ellipse withequal axes. In some embodiments, one axis of the ellipse (R₁) is alignedwith the instantaneous direction of motion of the survey vehicle at thelocation where the peak concentration is detected. The length of eachaxis of the ellipse may be chosen to be fixed or variable in a way thatis suitable to account for one or more of the effects that lead touncertainty in the detected peak gas location and/or uncertainty in leaklocation for near-vehicle leaks.

In some embodiments, the length of the axis of the ellipse that isaligned with the direction of motion (R₁) is scaled in proportion to thespeed of the vehicle. A fixed timing-delay offset between theconcentration and location measurements results in a positional errorthat scales directly with car speed. Consequently, scaling the ellipseaxis with the vehicle speed reflects an expected positional uncertaintydue to timing delay errors.

In some embodiments, the axis of the ellipse that is perpendicular tothe direction of motion (R₂) is scaled according to data representativeof wind speed, wind direction variability, and/or atmospheric stability.Such scaling reflects the observation that the distance at which upwindleaks may be detected can depend on the local wind speed as well as onthe degree of atmospheric stability. If a fixed length is chosen for theaxis perpendicular to the direction of vehicle motion, the length may bechosen to ensure that near-vehicle leaks fall within ellipse with achosen frequency (probability) under typical survey conditions. In suchcase, a suitable value for R₂ may be chosen to be between about 1 and 10meters, more particularly between about 3 and 8 meters, for exampleabout 6 meters. In some embodiments an appropriate length may be chosenby driving multiple times upwind of a source at various distances,repeating the process for multiple sources, and constructing anappropriate probability distribution.

Scaling the minor and/or major axes is a way to account for how thelikelihood of detecting the plume from a position upwind of the sourcechanges as a function of the wind speed, variability of the winddirection, or atmospheric stability conditions. The lighter the wind andmore variable the direction, the more likely it would be to detect thesource from a position upwind with respect to the mean wind direction.Additionally, the likelihood of detecting the source from an upwindposition may be a function of the degree of atmospheric stability. Themore unstable the atmosphere (closer to stability class A), the morelikely the plume dispersion is dominated by vertical mixing (as opposedto horizontal mixing) and the less likely it would be to detect thesource from a position upwind of the source. In some embodiments, suchscaling relationships may be determined empirically through systematicmeasurements.

In some embodiments, it may be desirable to require minimum values forthe lengths of both axes, to ensure the ellipse does not collapse into aline or point. In an exemplary embodiment, the minimum length of eachaxis may have a value between 6 and 16 meters, for example about 12meters (corresponding to a radius of 6 m in the case of a circle). Insome embodiments it may be desirable to set an upper limit on theeccentricity of the ellipse, for example for visualization/aestheticpurposes. In an exemplary embodiment, the ratio of the lengths of thesemimajor and semiminor axes may be limited to values between 1 and 4,with a preferred value of 2.

Survey Area Boundary Adjustments According to Wind and/or PositionUncertainties

In some embodiments, the determination of a boundary of a survey area 80as described above with reference to FIGS. 9-11 may take into accountdetermined uncertainties in wind direction and measurement locationdeterminations. The effect of including the measurement uncertainty onthe probability density in FIG. 11 is to make the probability densitydistribution wider, such that a larger range of angles between theta minand theta max would be needed to fulfill the probability condition. Ifone maintains the same probability threshold as described above, the neteffect is a reduction in the width of the field of view (FOV).

FIG. 25 shows an exemplary sequence of steps performed by at least oneprocessor to generate a display according to determined variabilityand/or measurement uncertainty indicators, according to some embodimentsof the present invention. In a step 520, one or more parametervariability indicators are determined as described above. In a step 522,one or more measurement uncertainty indicators are determined asdescribed above. In a step 524, a width is determined for each searcharea indicator according to the determined variability and/ormeasurement uncertainty indicators as described above. In a step 526,the length(s) of one or both central LISA ellipse axes are determinedaccording to the determined variability and/or measurement uncertaintyindicators as described above. In a step 528, a survey area boundary isdetermined according to the determined variability and/or measurementuncertainty indicators as described above. In a step 530, determineddisplay parameters are transmitted to a display device for display. In astep 532, the display device renders a display as shown above accordingto the received display parameters.

In some embodiments, the steps shown in FIG. 25 other than the finalstep 532 are performed on a cloud server or other device remotelyconnected to a display device present in a survey vehicle or otheron-site location, while step 532 is performed on a local or remotedisplay device. In some embodiments, at least parts of some of the stepsprior to step 532 may also be performed locally, for example using ascripting language such as Javascript. In cases where there is noconnection to the cloud (due to poor cell coverage, for example) thesurvey can still be conducted and the results still seen by the user inreal time.

It will be clear to one skilled in the art that the above embodimentsmay be altered in many ways without departing from the scope of theinvention. For example, gas leaks may include, but are not limited to:leaks from gas pipes or transportation systems (e.g., natural gasleaks), leaks from gas processing or handling facilities, and emissionsfrom gas sources into the environment (e.g., pollution, gas emissionfrom landfills, etc.). Gas concentration measurements are preferablyperformed rapidly (e.g., at a rate of 0.2 Hz or greater, more preferably1 Hz or greater). This enables the concept of driving a vehicle atnormal surface street speeds (e.g., 35 miles per hour) whileaccumulating useful gas concentration and wind measurement data.However, embodiments of the invention do not depend critically on thegas detection technology employed. Any gas concentration measurementtechnique capable of providing gas concentration measurements can beemployed in some embodiments.

Although the gas concentration measurements are preferably performedwhile the gas measurement device is moving, at least some gasconcentration measurements can be performed while the gas concentrationmeasurement device is stationary. Such stationary gas concentrationmeasurements may be useful for checking background gas concentrations,for example. While real-time measurements are preferred, post analysisof more sparsely sampled data, e.g., via vacuum flask sampling and lateranalysis via gas chromatography or other methods, may be used in someembodiments. Optionally, measurements can be made on different sides ofthe road or in different lanes to provide more precise localization ofthe leak source. Optionally, the present approaches can be used inconjunction with other conventional methods, such as visual inspectionand/or measurements with handheld meters to detect emitted constituents,to further refine the results. Optionally, measurements can be made atreduced speed, or with the vehicle parked near the source, to provideadditional information on location and/or source attribution.

Optionally, the system can include a source of atmosphericmeteorological information, especially wind direction, but also windspeed or atmospheric stability conditions, either on-board the vehicleor at a nearby location. The stability of the atmospheric conditions canbe estimated simply from the wind speed, the time of day, and the degreeof cloudiness, all of which are parameters that are available either onthe vehicle or from public weather databases. Optionally, the apparatuscan include an on-board video camera and logging system that can be usedto reject potential sources on the basis of the local imagery collectedalong with the gas concentration and wind data. For example, a measuredemissions spike could be discounted if a vehicle powered by natural gaspassed nearby during the measurements. Optionally, repeated measurementsof a single location can be made to provide further confirmation (orrejection) of potential leaks. Accordingly, the scope of the inventionshould be determined by the following claims and their legalequivalents.

What is claimed is:
 1. A natural gas leak detection system comprising:at least one hardware processor and associated memory configured togenerate display content according to gas concentration and associatedwind direction and wind magnitude data characterizing a gasconcentration measurement run performed by a mobile gas measurementdevice; and a display device coupled to the at least one hardwareprocessor and associated memory, the display device configured topresent the display content; wherein generating the display contentcomprises identifying at least one angular search area suspected to havea natural gas leak source and extending upwind from a gas concentrationmeasurement point, the angular search area having an axis indicating arepresentative wind direction relative to a geo-referenced location ofthe gas concentration measurement point, the angular search area havinga width relative to the axis, wherein the width is indicative of a winddirection variability characterizing a plurality of wind directionmeasurements in an area of the gas concentration measurement point;identifying a local potential leak source area comprising the gasconcentration measurement point; and graphically highlighting a part ofa display of a street map selectively within the identified angularsearch area and local potential leak source area.
 2. The system of claim1, wherein the potential local leak source area comprises an areadownwind from the gas concentration measurement point.
 3. The system ofclaim 1, wherein the local potential leak source area is identifiedaccording to a survey vehicle speed characterizing the gas concentrationmeasurement point.
 4. The system of claim 3, wherein the local potentialleak source area is identified according to a wind speed characterizingthe gas concentration measurement point.
 5. The system of claim 3,wherein the local potential leak source area is identified according toa survey vehicle direction characterizing the gas concentrationmeasurement point.
 6. The system of claim 3, wherein the local potentialleak source area is identified according to a wind directioncharacterizing the gas concentration measurement point.
 7. The system ofclaim 1, wherein the local potential leak source area is a closed areahaving a rounded boundary.
 8. The system of claim 1, wherein the localpotential leak source area is shaped as a circle.
 9. The system of claim8, wherein the circle has a radius representing a geographical distancebetween 10 and 30 feet.
 10. The system of claim 9, wherein the radiusrepresents a geographical distance between 15 and 25 feet.
 11. Thesystem of claim 1, wherein the local potential leak source areaindicator has a shape elongated along a measurement path at thegeo-referenced location of the gas concentration measurement point. 12.The system of claim 1, wherein the local potential leak source area isshaped as an ellipse.
 13. The system of claim 12, wherein a major axisof the ellipse is tangential to a measurement path at the geo-referencedlocation of the gas concentration measurement point.
 14. The system ofclaim 13, wherein a length of the major axis of the ellipse isrepresentative of an uncertainty in the determination of thegeo-referenced location along a tangent to the measurement path at thegeo-referenced location of the gas concentration measurement point. 15.The system of claim 13, wherein a length of the major axis of theellipse is determined such that an estimated frequency at which near- orunder-vehicle leak locations fall inside a boundary of the ellipsesatisfies a probability condition.
 16. The system of claim 13, wherein alength of the major axis of the ellipse is determined according to asurvey vehicle speed characterizing the gas concentration measurementpoint.
 17. The system of claim 13, wherein a length of the minor axis ofthe ellipse is determined according to a wind speed characterizing thegas concentration measurement point.
 18. The system of claim 13, whereina length of the minor axis of the ellipse is determined according todata representative of local atmospheric stability at the gasconcentration measurement point.
 19. The system of claim 13, wherein alength of a minor axis of the ellipse is determined according to anuncertainty in the determination of the geo-referenced location along adirection perpendicular to the measurement path at the geo-referencedlocation of the gas concentration measurement point.
 20. The system ofclaim 13, wherein a length of a minor axis of the ellipse is determinedaccording to a characteristic distance from which upwind leaks near themeasurement path are detectable.
 21. The system of claim 13, wherein alength of the minor axis of the ellipse is determined such that anestimated frequency at which near- or under-vehicle leak locations fallinside a boundary of the ellipse satisfies a probability condition. 22.The system of claim 1, wherein the width of the search area indicator isdetermined according to a survey vehicle speed and a wind speedcharacterizing the gas concentration measurement point.
 23. The systemof claim 22, wherein the width of the search area indicator isdetermined according to a function that increases with the surveyvehicle speed characterizing the least one gas concentration measurementpoint, and decreases with the wind speed characterizing the gasconcentration measurement point.
 24. The system of claim 1, wherein thewidth of the search area indicator is determined according to an angularstandard deviation characterizing the plurality of wind directionmeasurements.
 25. The system of claim 1, wherein the display contentfurther comprises: at least one path on the map indicating a route oftravel by the mobile gas measurement device, and at least one indicatoron the map that indicates a surveyed area for at least one potential gasleak source, wherein the surveyed area adjoins the path and extends in asubstantially upwind direction from the path, wherein the surveyed areais determined according to: a wind direction variability characterizinga plurality of wind direction measurements performed along the route oftravel; and a measurement uncertainty characterizing a plurality of winddirections relative to ground determined from the plurality of winddirection measurements.
 26. A non-transitory computer-readable mediumencoding instructions which, when executed by at least one hardwareprocessor and associated memory, cause the at least one hardwareprocessor and associated memory to generate display content forpresentation on a display device, the display content being generatedaccording to gas concentration and associated wind direction and windmagnitude data characterizing a gas concentration measurement runperformed by a mobile gas concentration measurement device, whereingenerating the display content comprises: identifying at least oneangular search area suspected to have a natural gas leak source andextending upwind from a gas concentration measurement point, the angularsearch area having an axis indicating a representative wind directionrelative to a geo-referenced location of the gas concentrationmeasurement point, the angular search area having a width relative tothe axis, wherein the width is indicative of a wind directionvariability characterizing a plurality of wind direction measurements inan area of the gas concentration measurement point; identifying a localpotential leak source area comprising the gas concentration measurementpoint; and graphically highlighting a part of a display of a street mapselectively within the identified angular search area and localpotential leak source area.
 27. A system comprising at least onehardware processor and associated memory configured to generate displaycontent for presentation on a display device, the display content beinggenerated according to gas concentration data characterizing a gasconcentration measurement run performed by a mobile gas concentrationmeasurement device, wherein generating the display content comprises:identifying a local potential leak source area comprising the gasconcentration measurement point, wherein identifying the local potentialleak source area comprises determining an extent of the local potentialleak source area along a vehicle movement direction at the gasconcentration measurement point according to a vehicle speed at the gasconcentration measurement point; and graphically highlighting a part ofa display of a street map selectively within the identified localpotential leak source area.